Question

A central angle θ in a circle with a radius of 6.4 centimeters intercepts an arc with a length of 8 centimeters. What is the radian measure of θ ? Enter your answer, as a decimal, in the box.

Answer 1

Radius of the circle = r = 6.4 cm
Length of the arc = s = 8 cm
Measure of angle formed by the arc = θ = ?

The radius of the circle, arc length and the angle made by the arc at the center of the circle are related by the equation:

s = rθ

From here we can find θ by:

θ = s/r

Using the values, we get:

θ = 8/6.4

θ= 1.25 radians

Thus the radian measure of the angle θ made by the arc will be 1.25 radians